Error vector magnitude optimization with cubic metric reduction and out-of-band radiation constraints in OFDM systems

Orthogonal frequency division multiple (OFDM) has been introduced into long term evolution (LTE) because of its high spectral efficiency and robust anti-multipath fading ability. However, a major drawback of OFDM signals is high fluctuations of signal envelope. Peak-to-average power ratio (PAPR) is a well-known measure for the envelope fluctuations. Recently, another metric named cubic metric (CM) has been proposed as a more accurate measure to quantify the fluctuations of signal envelope. This paper proposes a CM reduction method based on convex optimization technique. We consider comprehensively the performance in CM reduction, in-band distortion, and out-ofband radiation with an optimization model, whose objective is to achieve the minimum error vector magnitude (EVM) subject to CM and spectral mask constraints. A customized interior point method (IPM) is proposed to solve the optimization problem. Simulation results validate the good performance of the proposed method in CM reduction and convergence rate. It is shown that, with only three iterations, the proposed algorithm can achieve the minimum EVM under the conditions of given CM and out-of-band radiation.

I. Introduction

Due to high spectral efficiency and robustness in the multipath environment, orthogonal frequency division multiple (OFDM) has been adopted by 3GPP as the standard of Long Term Evolution (LTE) downlink. However, one of the major disadvantages of OFDM is large envelope fluctuations, which has negative impact on its applications [1]. To reduce the impairment of large envelope fluctuations, power amplifier (PA) usually needs the back-off operation. However, this operation degrades power efficiency. In order to improve the efficiency of PA, a common method is to decrease the envelope fluctuations of OFDM signals. Peak-to-average power ratio (PAPR) and cubic metric (CM) are two well-known measures of quantifying the envelope fluctuations. It has been adopted by 3GPP that CM is a more accurate measure than PAPR when used to predict the necessary backoff of PA [2]. The reason is that PAPR only focuses on the peak amplitude of signals while CM considers the fact that the signal distortion mainly results from the third-order nonlinear intermodulatoin product of PA.